= Arrested cubic buoyancy profile
{title2=$G=Q^2(z+H)^3/(27d^8)$}
An upward <volume flux> $Q$ and a downward turbulent buoyancy transport $d^4(G_z)^{3/2}$ balance in a steady reactor. Matching $G=G_z=0$ below $-H$ gives $QG=d^4(G_z)^{3/2}$. Integrating yields the cubic profile above the front. If downward source <buoyancy flux> is $B_s$, then $H=3d^{8/3}B_s^{1/3}/Q$. The corresponding <eddy diffusivity> is $K=Q(z+H)/(3d^2)$. All these prefactors use the same area and mixing-length normalization; an actual cross-sectional area $S$ replaces the denominator in $K$ by $3S$.
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